Modified couple stress theory in orthogonal curvilinear coordinates

Hamed Farokhi, Mergen H. Ghayesh*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

28 Citations (Scopus)
44 Downloads (Pure)


The formulations for the modified couple stress theory (MCST) are consistently derived in general orthogonal curvilinear coordinate systems. In particular, the expressions for the rotation vector, higher-order strain, and stress tensors, i.e., the rotation gradient tensor and the deviatoric part of the symmetric couple stress tensor, and the classical strain and stress tensors are derived for an arbitrary orthogonal curvilinear coordinate system. Additionally, using the theory of surfaces, the formulations for the MCST are derived for general doubly curved coordinates, which are more convenient to use for shells of arbitrary curvature. The expressions for special cases, i.e., cylindrical and spherical shells, are obtained. The MCST expressions derived in this study are comprehensive and generally and can be used for consistent utilisation of the MCST in any orthogonal curvilinear coordinate system.

Original languageEnglish
Pages (from-to)851-869
JournalActa Mechanica
Issue number3
Early online date7 Dec 2018
Publication statusPublished - Mar 2019


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